There are a lot of advocates of absolutely strict alternate picking, like Chris Thile. I've been practicing that for a couple of weeks now, and I'm at the point where I can play just about anything without slipping into economy picking by accident. There's one thing I keep getting stuck on, though: when I start a new phrase, I want to start with a downstroke, even if I just played a downstroke. It feels so much more natural, particularly if it's been more than a measure since the last phrase; but it takes away from the big benefit of alternate picking, which is that I always know which direction to go next.

So, do hardcore alternate pickers actually alternate through the whole song? Like, what if you end a phrase on a downstroke and your next phrase is 30 seconds later, at the beginning of a verse? Where's the limit?

I know each instrument has its own norms about picking. I play guitar, but I'd be interested to hear what mando players and others do as well.

4 Answers
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No, once you have a significant rest you don't need to alternate, and I'd still think of it as "strict alternate picking".

Note: I tend to think of alternate picking as down on the beats and
up on the 8th notes between beats (or the same idea with respect to 8th and 16ths); not necessarily that every string attack come from an alternate direction. If the next phrase starts on the "and" of a beat, then strict alternate picking would mean to pick upwards on that note.

Alternate picking should only be utilized of for the duration of 1 phrase. The first note of the next phrase should then be picked in a manner that best serves the phrase itself...be it an upstroke or downstroke.

When doing strict alternate picking, is it OK to play a downstroke twice in order to start a new phrase on a downstroke?

Absolutely yes, if this is what you feel, this is fine. You have to play your way. If your way is zelously strict alternate-picking then feel free to do that instead, but right-hand technique is not a religious doctrine.

It feels so much more natural...

Exactly! You can train yourself into finding strict alternate-picking more natural if that's your bag, but this is for you to decide. Do what you feel is right. Right-hand technique is not a religious doctrine.

do hardcore alternate pickers actually alternate through the whole song?

Some do, some don't.

I imagine Chris Thile espouses this technique because it works for him, if it works for you too then great. If you want to learn this technique go for it. If you find it more natural/expressive/fun to slip in the occasional economy-pick then that's great too because right-hand technique is not a religious doctrine.

I don't understand the how "strict alternate picking" is useful. If you have to focus on every stroke, and even go against your natural tendency sometimes, it's probably a bad idea. Economy picking is considered bad sometimes because it's harder to play the correct durations with it, but strict alternate picking can feel confusing an unnatural sometimes.

Also note that if you play two consecutive downstrokes or upstrokes it doesn't necessarily mean that you're economy picking. Economy picking is when you hit one note, then another one within the same upstroke or downstroke. If you use two downstrokes in succession it's not economy picking.

The technique that feels the most natural for me is to keep a steady 16th note up and down motion with my right hand, and only hit the string with the pick when I need to. It's like tremolo picking but, but you keep the pick away from the strings on rests or in the middle of notes longer than 16ths. With this method it's hard to mess up the rhythm, and it feels extremely natural. The hard part is learning not to hit the strings by mistake when you don't need to.

So to answer your question, sticking to alternate picking 100% of the time can be bad. It's ok to break up the pattern on rests or any note longer than a 16th if it makes you comfortable. Ultimately you want a technique that maximizes your accuracy and speed. A confusing picking technique (like pure alternate picking) doesn't help much in this area. While economy picking can help with speed, it doesn't help with accuracy. So it's ok to use it in a short lick that would be a bit too fast for alternate picking. You need to experiment with every possible picking technique and understand it's advantages and disadvantages. You've tried economy picking, strict alternate picking; now try to play alternate picking your way (break it up whenever you want but do not hit two consecutive note with the same motion), also try the technique I recommended above (players like Jimmy Hendrix and Stevie Ray Vaughan use it a lot). You probably should combine these techniques depending on the scenario, instead of constraining yourself to the same rule the hole time.